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PTT 201/4 THERMODYNAMIC SEM 1 ( 2013/2014). CHAPTER 7: Entropy. Objectives. • Apply the second law of thermodynamics to processes. • Define a new property called entropy to quantify the second- law effects. • Calculate the entropy changes that take place during.

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PTT 201/4 THERMODYNAMIC SEM 1 ( 2013/2014)

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SEM 1 (2013/2014)

  • CHAPTER 7:

  • Entropy


• Apply the second law of thermodynamics to processes.

• Define a new property called entropy to quantify the second-law effects.

• Calculate the entropy changes that take place during

processes for pure substances, incompressible substances,and ideal gases.

• Examine a special class of idealized processes, called

isentropic processes, and develop the property relations forthese processes.

• Derive the reversible steady-flow work relations

• Introduce and apply the entropy balance to various systems.


Entropy, S


A measure of molecular disorders ormolecular randomness in a system

The larger value of S, the more molecular randomness of particles in the system

The level of molecular

disorder (entropy) of substance increases asit melts or evaporates.

The paddle-wheel work done on a gas increases the level ofdisorder (entropy) of the gas, and thus energy is degradedduring this process.

During a heat

In the absence of

transfer process, the

friction, raising aweight by a rotating

net entropy

increases. (Theincrease in the

shaft does not

create any disorder(entropy), and thusenergy is not

entropy of the coldbody more than

offsets the decrease

degraded during thisprocess.

in the entropy of

the hot body.)4

ENTROPY (How to measure the entropy-

based-on from Clausius inequality)




definitionof entropy

The system considered inthe development of theClausius inequality.

The equality in the Clausius inequality holdsfor totally or just internally reversible cyclesand the inequality for the irreversible ones.

(based-on energy balance)


The entropy change between two

specified states is the same whether

the process is reversible or irreversible.

∆S can be positive/negative depending on the direction of heat transfer:

Q transfer to a system: ∆S increase (+ve)

Q transfer from a system: ∆S decrease (-ve)

A Special Case: Internally ReversibleIsothermal Heat Transfer Processes

This equation is particularly useful for determiningthe entropy changes of thermal energy reservoirs at constant temperature.


EXAMPLE 7-1Entropy Change during an Isothermal Process

A piston-cylinder device contains a liquid-vapor mixture of water at 300 K. During a constant pressure process, 750 kJ of heat is transferred to the water. As a result, part of the liquid in the cylinder vaporizes. Determine entropy change of the water during this process

Some Remarks about Entropy

1.Processes can occur in a certaindirection only, not in any

direction. A process must proceed in the direction thatcomplies with the increase of entropy principle, that is, Sgen ≥

0. A process that violates this principle is impossible.

2.Entropy is a nonconserved property, and there is no such

thing as the conservation of entropy principle. Entropy isconserved during the idealized reversible processes only andincreases during all actual processes.

3.The performance of engineering systems is degraded by the

presence of irreversibilities, and entropy generation is ameasure of the magnitudes of the irreversibilities during thatprocess. The greater the extent of irreversibilities, the

greater the entropy generation. It is also used to

establish criteria for the

performance of engineering devices.


EXAMPLE 7-2Entropy Generation during Heat Transfer Process

A heat source at 800 K losses 2000 kJ of heat to a sink at (a) 500 K and (b) 750 K. Determine which heat transfer process is more irreversible.


Entropy is a property, and thus thevalue of entropy of a system is fixedonce the state of the system is fixed.

Schematic of the T-s diagram for water.

Entropy change

The entropy of a pure substanceis determined from the tables

(like other properties).


Where m is specified mass

EXAMPLE 7-3Entropy Change of a Substance in a Tank

A rigid tank contains 5 kg of refrigerant-134a initially at 20˚C and 140 kPa. The refrigerant is now cooled while being stirred until its pressure drops to 100 kPa. Determine the entropy change of the refrigerant during this process.


A process during which the entropy remains constant is calledan isentropic process.

During an internally

reversible, adiabatic

(isentropic) process, theentropy remains constant.

The isentropic process appears as avertical line segment on a T-s diagram.


EXAMPLE 7-5Isentropic Expansion of Steam in a Turbine

Steam enters an adiabatic turbine at 5 MPa and 450˚C and leaves at a pressure of 1.4 MPa. Determine the work output of the turbine per unit mass of steam if the process is reversible.


Derived from

equation 7-23,

Liquids and solids can beapproximated as

or known asGibbs equation

incompressible substances

since their specific volumesremain nearly constant

during a process.

For an isentropic process of an incompressible substance


EXAMPLE 7-7Effect of Density of a Liquid on Entropy

Liquid methane is commonly used in various cryogenic applications. The critical temperature of methane is 191 K to keep it in liquid phase. The properties of liquid methane at various temperatures and pressures are given in Table 7-1. Determine the entropy change of liquid methane as it undergoes a process from 110 K and 1 MPa to 120 K and 5 MPa (a) using tabulated properties and (b) approximating liquid methane as an incompressible substance. What is the error involved in the latter case?


From the first T ds relation (Eq 7-25). From the second T dsrelation (Eq 7-26)

Ideal gas



Constant Specific Heats (Approximate Analysis)

Entropy change of an ideal gas on a

unit-mole basis

Under the constant-specific-

heat assumption, the specificheat is assumed to be constantat some average value.


Variable Specific Heats (Exact Analysis)

We choose absolute zero as the reference

temperature and define a function s° as

On a unit-mass basis

The entropy of an ideal

gas depends on both T

and P. The function sorepresents only the

On a unit-mole basis


part of entropy.


EXAMPLE 7-9Entropy Change of an Ideal Gas

Air is compressed from an initial state of 100 kPa and 17˚C to a final state of 600 kPa and 57˚C. Determine the entropy change of air during this compression process by using (a) property values from the air table and (b) average specific heats.

Isentropic Processes of Ideal Gases

Constant Specific Heats (Approximate Analysis)

Setting this eq. equal to

zero, we get

The isentropic relations of idealgases are valid for the isentropicprocesses of ideal gases only.


Isentropic Processes of Ideal Gases

Variable Specific Heats (Exact Analysis)

Relative Pressure and Relative Specific Volume

The use of Prdatafor calculating the

exp(s°/R) isthe relativepressure Pr.

final temperatureduring an isentropicprocess.

Refer Table A-17

Pv=RT (ideal gas relationship),


The use of vrdata for

calculating the finaltemperature during an

T/Pris the relativespecific volume vr.

isentropic process


EXAMPLE 7-11 Isentropic Compression of an Ideal Gas

Helium gas is compressed by an adiabatic compressor from an initial state of 100 kPa and 10˚C to a final temperature of 160˚C in a reversible manner. Determine the exit pressure of helium.




From energy balance

for steady-state device

(- sign means work is produced by the system)

When kinetic and

potential energiesare negligible

(+ sign means work is done on the system)

The larger the


volume, thegreater thework

For the steady flow of a liquid through adevice that involves no work interactions(such as a pipe section), the work term iszero (Bernoulli equation):

Reversible workrelations for steady-flow and closedsystems.

produced (orconsumed) bya steady-flowdevice.


EXAMPLE 7-12 Compressing a Substance in the Liquid versus Gas Phases

Determine the compressor work input required to compress stem isentropically from 100 kPa to 1 MPa, assuming that the steam exists as (a) saturated liquid and (b) saturated vapor at the inlet state.


Entropy Change of a

System, ∆Ssystem

Energy and entropybalances for a system

Mechanisms of Entropy Transfer, Sin and Sout

1 Heat Transfer

Entropy transfer by heat transfer:

Entropy transfer by work:

Heat transfer is always accompanied byentropy transfer in the amount of Q/T,where T is the boundary temperature.

No entropy accompanies work as it crossesthe system boundary. But entropy may begenerated within the system as work is

dissipated into a less useful form of energy.20

2 Mass Flow

Entropy transfer by mass:

When the properties of the masschange during the process

Mass contains entropy as well asenergy, and thus mass flow into or

out of system is always

accompanied by energy andentropy transfer.


Entropy Generation, Sgen

Entropy generationoutside system

boundaries can beaccounted for by

writing an entropy

balance on an

extended system thatincludes the system

and its immediate


Mechanisms of entropy transfer for ageneral system.


Closed Systems

The entropy change of a closed system during a process is equal to thesum of the net entropy transferred through the system boundary by heat

transfer and the entropy generated within the system boundaries.


Control Volumes

The entropy of a

substance alwaysincreases (or

remains constant in

The entropy of a controlvolume changes as a resultof mass flow as well as heattransfer.

the case of a

reversible process)as it flows through asingle-stream,

adiabatic, steady-

flow device.


EXAMPLE 7-20Entropy Generation in a Heat Exchanger


Try the examples in the next slides

EXAMPLE 7-17Entropy Generation in a Wall

EXAMPLE 7-18Entropy Generation During a Throttling Process

EXAMPLE 7-19Entropy Generated when a Hot Block is Dropped in a Lake


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